The very recent discovery of a new linear instability in dilute viscoelastic rectilinear flows at high \(Wi=O(20)\)  (in pipes by [1]} and channels by [2]}) seems highly relevant. Such `straight' flows had always been believed linearly stable due to the absence of curved streamlines [3]}, [4]}, [5]}, [6]} although there had been some evidence of instability to finite-amplitude disturbances at low \(Re\)  [7]}, [8]}, [9]}, [10]}.
Significantly, the neutral curve for this instability lies in a region of the \((Wi,Re)\)  parameter space between where EIT and ET are believed to exist.
The instability was initially only found above \(Re \approx 63\)  in pipe flow in the Oldroyd-B model [1]}, [4]}, suggesting that it needs some inertia to function.
However, the corresponding instability in channel flow was found to have no such finite-\(Re\)  threshold, although for Oldroyd-B fluids, the instability is restricted to ultra dilute solutions with \(\beta \gtrsim 0.99\) , and very large \(Wi=O(10^3)\)  [2]}, [14]}. Subsequently, these conditions have been relaxed to a more physically-relevant critical \(Wi\gtrsim 110\)  at \(\beta \approx 0.98\) , by limiting the maximum extension of the polymers (\(L_{max}=70\) ) in a FENE-P model [15]}.
This suggests that a purely elastic instability can smoothly morph into an elasto-inertial one, where inertia plays a role but the instability is found to only derive its energy through elastic terms. This remains the case even as high as \(Re=O(1000)\)  [15]}.
While this new instability is active for a wide range of parameter values, it does not appear to overlap with areas where either EIT or ET have been found, consistently appearing at much higher \(Wi\)  at a given \(Re\) . Therefore, the question of its relevance to these nonlinear states remains open.
